the Jester
Legend
I usually let PCvPC situations play themselves out unless I get the impression it's really a player v player personality clash. Then I step in and tell the players to knock it off. Sometimes, however, it's not easy to tell if it's getting personal.
One way to find out may be coming up for you. When it comes time to split the party (or as it approaches), tell your players it's fine to dissolve the adventuring party and have the PCs go their separate ways, but you won't DM two separate groups. You don't have the time. One of the two groups must make up new PCs and reform an adventuring group with the old PCs. If there's a lot of balking at that and still no willingness to reform, then it may be less a PC personality issue and more a player issue. If it's totally a PC issue, then I think players would be willing to say "Yes, this PC doesn't fit the party very well. I'll make up one that does."
What do you recommend if each player insists the other group should be the one to make new pcs?
Bear in mind (from the sounds of it) that two other players are involved and one of them is almost certainly going to get stuck making a new pc as well if you do things this way.